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Math Help - Reducing Fractions

  1. #1
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    Reducing Fractions

    Reduce to the lowest terms.

    _x + 4__ __x + 4__
    x^2-x-12 + x^2 + 5x + 6


    __3_ __c - 4___ __5__
    4c+2 - 2c^2+c - 6c
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  2. #2
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    Quote Originally Posted by pashah
    Reduce to the lowest terms.

    _x + 4__ __x + 4__
    x^2-x-12 + x^2 + 5x + 6


    __3_ __c - 4___ __5__
    4c+2 - 2c^2+c - 6c
    Hello, pashah,

    1rst problem:

    Factorize the denominators and you'll get:
    \frac{x+4}{(x-4)(x+3)}+\frac{x+4}{(x+2)(x+3)}. Put the common factor in front of a bracket:
    \frac{1}{x+3}\cdot \left(\frac{x+4}{x-4}+\frac{x+4}{x+2}\right). Now rearrange the terms in the bracket. You can factorize the numerator again. The final result should be:
    \frac{2}{x+3}\cdot \left(\frac{(x-1)(x+4)}{(x-4)(x+2)}\right). But as you see, you can't simplify this fraction (maybe there is a typo?)

    2nd problem
    Factorize (if possible) the denominators:
    \frac{3}{2(2c+1)}-\frac{c-4}{c(2c+1)}-\frac{5}{6c}
    The common denominator is 6c(2c+1). Expand all fractions:
    \frac{3\cdot 2c}{6c(2c+1)}-\frac{6(c-4)}{6c(2c+1)}-\frac{5(2c+1)}{6c(2c+1)}
    Add all terms of the numerators:
    \frac{-10c+19}{6c(2c+1)}

    Greetings

    EB
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